Abstract
This paper proposed a calculation method for bolts reinforcement of tunnel face under the seepage condition. The existence of seepage in tunnel engineering may greatly reduce the stability of tunnel face, and bolts reinforcement technology is widely used in traditional tunnel engineering. In this paper, a 3D rotational failure mechanism is proposed by the kinematics method combined with the discretization technique. The pore water pressure was added in the energy calculation based on the empirical distribution formula of water head. The interaction between soil and bolts is simulated by using a finite thickness interaction region. The method was compared with the published works in order to verify the effectiveness. The influence of the bolt length, the bolt strength, the hydraulic head size, the face height and the soil parameters are given in the form of some graph.
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Abbreviations
- c :
-
Cohesion
- c g :
-
Grout cohesion
- D :
-
Work rate of the energy consumption
- H :
-
Height of the tunnel face
- h F :
-
Piezometric head distributing
- h 0 :
-
Initial level of underground water
- L :
-
Bolt length
- L z :
-
Bolt length inside the failure mechanism
- m i :
-
Number of bolts in each row
- n :
-
Bolt density
- r A :
-
Length of radial line OA
- r B :
-
Length of radial line OB
- r m :
-
Length from rotational center O to the center of a circle
- R :
-
The radius of a circle
- S AB :
-
Area of the elliptic appearance at the interface between the failure mechanism and the tunnel face
- S v :
-
Horizontal spacing of bolts
- S h :
-
Vertical spacing of bolts
- s h :
-
Number of bolt rows
- T m :
-
Tensile yield strength
- T p :
-
Pullout force
- v :
-
Velocity vector
- v k :
-
Velocity at the failure surface
- W b :
-
Power done by the bolts
- W s1 :
-
Power in front of the tunnel face caused by penetration
- W s2 :
-
Power above the tunnel face caused by penetration
- W γ :
-
Gravity power
- α :
-
Interaction coefficient between bolt and soil
- β k :
-
Angle between the velocity vk and the reinforcement
- γ :
-
Unit weight of soil
- γ w :
-
Unit weight of water
- Δh :
-
Difference value between hF and h0s
- δ :
-
Width of the interaction zone
- θ A :
-
Angle between vertical plane and the segment OA
- θ B :
-
Angle between vertical plane and the segment OB
- θ E :
-
Angle between vertical plane and the segment OE
- ϕ :
-
Bolt diameter
- φ :
-
Friction angle
- τ m :
-
Ultimate grout cohesion of bolt-soil interfacial surface
- ω :
-
Angular velocity
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Liu, J., Liu, L. Stability of Tunnel Face Reinforced by Bolts under Seepage Flow Conditions. KSCE J Civ Eng 26, 977–986 (2022). https://doi.org/10.1007/s12205-021-1116-4
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DOI: https://doi.org/10.1007/s12205-021-1116-4